Download The information content of an open limit-order book

THE INFORMATION CONTENT OF
AN OPEN LIMIT-ORDER BOOK
CHARLES CAO*
OLIVER HANSCH
XIAOXIN WANG
Using data from the Australian Stock Exchange, the authors assess the information
content of an open limit-order book with a particular focus on the incremental
information contained in the limit orders behind the best bid and offer. The
authors find that the order book is moderately informative—its contribution to
price discovery is approximately 22%. The remaining 78% is from the best bid and
offer prices on the book and the last transaction price. Furthermore, the authors
find that order imbalances between the demand and supply schedules along the
book are significantly related to future short-term returns, even after controlling
for the autocorrelations in return, the inside spread, and the trade imbalance.
© 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:16–41, 2009
The authors thank Geoffrey Booth, Tarun Chordia, Ian Domowitz, Joel Hasbrouck, Kenneth Kavajecz, Bruce
Lehmann, Mark Lipson, Chris Muscarella, Gideon Saar, Chester Spatt, Avanidhar Subrahmanyam, Robert
Webb (the Editor), an anonymous referee, and seminar participants at Penn State, Rutgers, George
Washington Universities, the Western Finance Association Meetings, the NBER-JFM Microstructure
Conference, the American Finance Association Meetings, and the 15th Annual Asia Pacific Futures Research
Symposium for their helpful comments. The authors are grateful to the Australian Stock Exchange and the
Securities Industry Research Centre Asia-Pacific for providing the data used in this study. The authors also
thank Morgan Stanley for providing the equity market microstructure research grant for this study.
*Correspondence author, Smeal College of Business Administration, Pennsylvania State University, 609 BAB,
University Park, PA 16802. Tel: 1-814-865-7891, Fax: 1-814 865 3362, e-mail: [email protected]
Received November 2006; Accepted February 2008
■
Charles Cao is a Smeal Chair Professor of Finance and Oliver Hansch is Assistant Professor of
Finance at Smeal College of Business Administration, Pennsylvania State University,
University Park, Pennsylvania.
■
Xiaoxin Wang is Assistant Professor of Finance, College of Business Administration, Southern
Illinois University, Carbondale, Illinois.
The Journal of Futures Markets, Vol. 29, No. 1, 16–41 (2009)
© 2008 Wiley Periodicals, Inc.
Published online in Wiley InterScience (www.interscience.wiley.com).
DOI: 10.1002/fut.20334
Open Limit-Order Book
INTRODUCTION
A majority of equity and derivative markets around the world are organized as
electronic limit-order books. Such equity markets include the Electronic
Communication Networks (ECNs) in the United States, the Toronto Stock
Exchange, and the Hong Kong Stock Exchange. Electronic trading platforms in
derivative markets have also gained popularity in recent years over the traditional open-outcry auctions. Chicago Mercantile Exchange’s (CME) Globex
platform, International Securities Exchange’s electronic option trading platform, and the single centralized limit-order book offered by Euronext.liffe are
all good examples. Electronic limit-order book has stepped up to the center
stage of the change in financial market structure. The London International
Financial Futures and Options Exchange Connect System has been adopted by
several derivative markets [e.g., the Chicago Board of Trade (CBOT), etc.].
Other markets, including the New York Mercantile Exchange, have migrated
their trading to the CME Globex electronic platform. Many derivative markets
have fully converted to an electronic trading system (e.g., the Sydney Futures
Exchange, the International Petroleum Exchange of London, and the Hong
Kong Futures Exchange).
With the growing popularity of electronic limit-order books in equity and
derivative markets, studying the trade prices and best quotes is no longer
enough for investors. Some derivative markets have released real-time limitorder books to investors for a monthly fee. Today, investors can view the top five
levels of depth for contracts listed on the CME (e.g., the popular E-Minis
futures) through the CME Globex Level II data feed, whereas the CBOT Level II
data feed allows traders to view the top ten levels of depth for contracts listed
on the CBOT (e.g., the Mini-Sized Dow Jones Industrial Average Futures).1
Among the reasons put forth for the popularity of an open limit-order book
is the greater transparency offered by these systems when compared with dealer
market settings. Although dealer markets usually rely upon dissemination of
only the dealers’ best quotes, a limit-order-book system allows its users to view
the depth at a number of price levels away from the market. These displayed
prices and quantities are instantaneously executable, typically. In dealer markets, however, prices for trades beyond the quoted size must be assessed
through negotiations with market makers. In addition, market makers may
choose to offer price improvement for trades up to a quoted size. In this study,
the authors study the information content of an open book, and examine
whether pre-trade transparency facilitates price discovery and helps investors
in predicting short-term price movements.
1
This difference in reporting depth for stock index futures contracts between CME and CBOT still exists
despite the merger of the two exchanges in 2007.
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Cao, Hansch, and Wang
Although the information content of a limit-order book has been the
subject of an active debate in the price discovery literature, there has been no
consensus about whether or not the order book is informative. On the one
hand, Glosten (1994), Rock (1996), and Seppi (1997) incorporated informed
traders into their models, assuming that they favor and actively submit market
orders. This suggests that the order book beyond the best bid and offer contains
little, if any, information. On the other hand, several recent studies suggest that
the order book is informative. Using an experimental design, Bloomfield,
O’Hara, and Saar (2005) found that in an electronic market, informed traders
submit more limit orders than market orders. Using SuperDot limit orders in
the TORQ database, Harris and Panchapagesan (2005) showed that the order
book is informative, and that New York Stock Exchange (NYSE) specialists use
the book information in ways that favor them over the limit-order traders.
Kaniel and Liu (2006) showed that informed traders prefer limit orders, and
that limit orders convey more information than market orders when the private
information is long-lived.
Regarding the question of whether pre-trade transparency facilitates price
discovery, the extant literature offers mixed evidence. Baruch (2005) provided a
theoretical model showing that an open limit-order book improves liquidity and
information efficiency of prices. Consistent with this prediction, Boehmer,
Saar, and Yu (2005) found that the deviations of transaction prices from the
efficient prices became smaller after the NYSE’s adoption of the open book system. In contrast, Madhavan, Potter, and Weaver (2005) found larger spreads
and higher volatility after the Toronto Stock Exchange disseminated the top
four price levels of the limit-order book in April 1990.
This study is part of the emerging literature on the information content of
the limit-order book. The authors are particularly interested in the incremental
information content of the book, over and above the information traditionally
available in a dealer market: i.e., the best bid and offer prices along with their
respective depths. Using order-book information from the Australian Stock
Exchange (ASX), the authors empirically assess the information content of an
open limit-order book from two perspectives.
First, the authors explore whether the limit-order book allows better estimations of a security’s value than simply the best bid and offer. If it does, how
much additional information can be gleaned from the book? By investigating
the relation among the midpoint of the best bid and ask, the transaction price,
and a quantity-weighted price based on limit orders, the authors find that the
order book beyond the first step is modestly informative and that price discovery
measures suggest that the contribution of the order book beyond the best bid
and offer is approximately 22%. Next, the authors examine whether the orderbook information is associated with future returns. In a repetitive regression
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Open Limit-Order Book
framework, the authors show that the imbalance in the limit buy and sell
orders beyond the inside market is useful and has additional power in explaining future short-term returns.
This study is organized as follows: the second section develops testable
hypotheses. The third section describes the institutional environment of the
ASX and the sample data. The information content of the order book is
assessed in the fourth section, and the fifth section provides evidence of the
association between returns and lagged imbalances between demand and supply. Concluding remarks are provided in the sixth section.
TESTABLE HYPOTHESES
Price discovery is one of the principal functions of a financial market. The
authors’ first hypothesis pertains to the price discovery function in a limit-order
book. Private information is incorporated into prices through trading by
informed traders, who can choose to employ market or limit orders in their
dynamic strategies. If informed traders use limit orders, especially limit orders
away from the inside market, their information is presumably reflected in the
book. If, however, informed traders use market orders, the orders in the book
may not contain any of their private information.
Models of limit-order books featuring privately informed traders typically
assume that they will favor market orders (Glosten, 1994; Rock, 1996; Seppi,
1997). Rock (1996) argued that, with short-lived private information, informed
traders will prefer market orders because they guarantee immediate execution.
Furthermore, given the direction of price movements conditional on the private
information, the execution of limit orders designed to exploit a trader’s informational advantage is unlikely. For example, an informed trader who knows
that the current market price is too high will expect the price to go downward
in the future, especially when the other traders learn the same information.
Thus, the likelihood of achieving execution for a limit sell order is relatively
small in this situation. Similarly, Angel (1997) and Harris (1998) argued that
informed traders are more likely to use market orders than are liquidity traders.
In contrast, Kaniel and Liu (2006) considered the case where private
information is long-lived and the number of traders who may discover the private information is small. They showed that informed traders may well prefer
limit over market orders, such that, in equilibrium, limit orders may convey
more information than market orders. One reason why informed traders are
reluctant to submit market orders is that submitting market orders signals
impatience and reveals too much information. Although their execution is certain and immediate, market orders incur higher trading costs than limit orders.
The two competing strands of models lead to the authors’ first hypothesis:
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Cao, Hansch, and Wang
Hypothesis 1: The Orders Behind the Best Bid and Ask Prices Contribute to
Price Discovery.
Evidence consistent with this hypothesis supports the prediction that
informed traders use limit orders as part of their trading strategies. On the contrary, if informed traders prefer to use market orders over limit orders, it will be
expected that their market orders may pick off any mis-priced limit orders until
the book reflects all available information.
The authors second hypothesis is concerned with the implications of the
order-book shape for short-term price dynamics, even in the absence of asymmetric information. The shape of the order book (i.e., the number of shares on
each price step and how far away price steps are from each other) gives
investors a concurrent picture of the market demand and supply. Specifically,
the asymmetries between the buy and sell side of the book indicate shifts in the
supply and demand curves caused by unobservable exogenous factors that
affect the price of a stock. Through observing the demand and supply, investors
have a better chance of guessing what these factors are and of predicting the
future price movements.
Harris (1990) considered two types of limit-order traders: pre-committed
and value-motivated traders. The former submit limit orders to reduce trading
costs, but will switch to using market orders if their orders remain unfilled for
too long. The latter express their valuations of the asset through their choice of
limit price. Both types of limit orders can convey information about future
price movements. A book imbalance caused by pre-committed traders may signal future price movements owing to these traders having to convert their
unfilled limit orders into market orders. For example, a heavier buy than sell
side would indicate a future price increase. An imbalance owing to the presence of value-motivated traders will reveal their valuations which will then
become impounded in prices. Harris (1990) also discusses a so-called “quotematching” strategy in which traders extract options values from the standing
limit orders by trading ahead of the heavier side of the book. The presence
of quote-matchers may thus create a link between asymmetries in the shape of
the two sides of the book and price dynamics.
Empirically, Huang and Stoll (1994) found that differences in quoted
depth between the bid and ask side do predict future price changes, especially
for price changes over short intervals. Recently, Chordia, Roll, and
Subrahmanyam (2002), Chordia and Subrahmanyam (2004), and Boehmer
and Wu (2006) documented the relation between order imbalance and future
price movements. The “order imbalance” in these studies refers to the difference
between quantity bought and sold. The Lee and Ready algorithm is usually
adopted to learn if a trade is buyer or seller initiated. As the authors study a
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Open Limit-Order Book
limit-order-book market with clearly stated buy and sell orders on each side of
the book, the ambiguity in classifying trade directions is avoided. The authors
broaden the scope of the investigation by including information on orders
beyond the best bid and offer. Kavajecz and Odders-White (2004) demonstrated that support and resistance levels coincide with peaks in depth on the limitorder book and that moving average forecasts reveal information about the
relative position of depth on the book. These issues lead to the following
hypothesis:
Hypothesis 2: Limit orders behind the best bid and ask prices contain information about short-term future price movements.
A rejection of the hypothesis indicates that the shape and make-up of the
limit-order book is not informative about short-term price movements beyond
those conveyed by the inside spread and depth.
DATA
The data used in this study are provided by the ASX via the Securities Industry
Research Centre Asia-Pacific. The ASX uses the fully computerized Stock
Exchange Automated Trading System (SEATS), which is based on the Toronto
Stock Exchange’s Computer Assisted Trading System.2 There are no dealers or
other designated liquidity providers on the ASX so that public orders can interact with each other directly. The ASX operates an open limit-order book, and
the order book is widely disseminated. Depending on the chosen level of detail,
SEATS Trading Screen users can view details of individual buy and sell orders
along the book or the aggregate depth at multiple price levels in real time, generally for at least the first ten steps. For example, E*trade-Australia and
TDwaterhouse-Australia provide their clients with the book truncated at the
tenth best step, and National Online Trading provides the book truncated at
the 20th step. More details of the order-book information are available to brokers and institutional investors, whereas the aggregate version is representative
of what online traders would be able to see. The openness of the book allows
the authors to examine whether the book information is valuable to investors.
Each day, the market goes through several stages. During the pre-opening
period from 7:00 A.M. to 10:00 A.M. (Eastern Standard Time), orders can be
entered into the system but no matching takes place. The ASX opens at 10:00 A.M.
with a procedure aimed principally at maximizing traded volume at the chosen
2
In 2006, ASX changed its name to Australian Securities Exchange after its merge with Sydney Futures
Exchange and SEATS was updated to the Integrated Trading System (ITS) workstation that can provide more
transactions per second; yet the feature of a pure open limit-order book remains.
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Cao, Hansch, and Wang
opening price. Stocks open sequentially in five groups, based on the alphabetical order of the ticker symbol, and normal trading begins immediately after the
conclusion of the opening algorithm for their group. This phase, during which
the vast majority of trading takes place, lasts until 4:00 P.M. Orders entered during normal trading hours are matched, resulting in trades, or they are stored in
the order book automatically. At 4:00 P.M., a five-minute period of “pre-close”
begins which is followed by the official single-price closing auction.
The authors obtain data covering the 100 most actively traded ASX stocks
for the month of March 2000 from the ASX intraday data set that provides historical details of all individual orders placed on SEATS as well as any of its
resulting trades. Each order and trade record includes information on the
price, size, and direction, time-stamped to the nearest one-hundredth of a second. Crucially, the data allow for the reconstruction of the limit-order book for
each stock at any point during the sample period. The authors’ procedure for
building the book is similar to the method described by Bessembinder and
Venkataraman (2004), who reconstruct the limit-order book on the Paris
Bourse. To avoid confounding effects from the opening and pre-close procedures,
the authors restrict their attention to the period from 10:15 A.M. to 4:00 P.M.
Because most investors at ASX can access the price and aggregate number of
shares up to the tenth step of the book, the authors construct the limit-order
book up to ten price steps away from the inside of the market.
Table I presents summary statistics for the 100 sample stocks. Reported
are cross-sectional distributions of daily trading activity. The average daily trading volume is 1.783 million shares, and the average number of trades is 349 per
day, with an average trade size of 5,279 shares. The average dollar spread is 2.82
cents and the relative spread is 0.28%. There is some cross-sectional difference
among the stocks. The most active stock has an average 1,323 transactions per
day, whereas the least active has only 63, and the daily share volume varies
TABLE I
Characteristics of the 100 Most Actively Traded Stocks on the Australian Stock Exchange
Mean
SD
Min.
Max.
Daily Share
Volume (Million)
Trade Size
(Share)
Number of Trades
Per Day
Dollar Spread
(Cents)
Relative
Spread (%)
1.783
1.967
0.127
12.791
5,279
5,158
1,186
37,532
349
266
63
1,323
2.82
2.28
0.53
11.26
0.280
0.179
0.060
0.838
Note. This table reports summary statistics for the 100 most actively traded stocks on the Australian Stock Exchange. The sample
period spans from March 1 to March 31, 2000. Reported above are cross-sectional mean, standard deviation, minimum and maximum
of daily share volume, trade size, daily number of trades, and time-weighted average of dollar (inside) bid–ask spread and relative
(inside) bid–ask spread.
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Open Limit-Order Book
from 127,000 to 12,791,000 shares. Liquidity measured as the inside bid–ask
spread shows an average range between 0.53 and 11.26 cents.
PRICE DISCOVERY IN THE LIMIT-ORDER BOOK
Summary Statistics of Order-Book Shape
At any point in time, a limit-order book contains a large number of buy and sell
orders. The aggregate market demand and supply are represented by these orders
as step functions of the accumulated number of shares offered at each price
level. To make the order-book data amenable for empirical analysis, the authors
use two summary measures designed to capture the most important features of
the step functions.
d
• The height of a step i on the demand side is §di Pid Pi1
. It is the price
difference between the ith and the (i 1)th best price (regardless of the
number of shares) on the buy side of the book. To compute the height of the
first step of the book, the authors denote the average of the best bid and offer
in the book by MID P0d.
• The length of a step i on the demand side of the book, Qid, is the aggregate
number of shares across all orders at price Pid.
• The heights and lengths of steps on the supply side, §is and Q si, are defined
analogously.
The authors then normalize a step height by the cumulative price difference
between the tenth step and MID. The authors also normalize a step length by
the cumulative length from the first step to the tenth step.
Table II reports the cross-sectional average of the step heights and lengths.
For both buys and sells, steps closer to the top of the book are generally longer.
Each of the first five steps in the book represents more than 10% of the respective side’s length, whereas the last step accounts for less than 4%. The second
step offers more depth than the first step for both the buy and sell sides. More
than 88% of the shares reside on the second step and beyond. This feature warrants a particular interest studying the orders that are located behind the top of
the book. The top steps are also lower (price increments are smaller) than the
away steps, and the step height increases monotonically along the order book.
The first step on each side is 1.41 cents—half the inside spread. The second step
goes up to 2.47 cents for buys and 2.39 cents for sells, and it increases to the
tenth step at 4.06 cents for buys and 4.88 cents for sells. In terms of percentage,
the first step makes up about 5% of the total height from the center top of the
book to the end of step 10, whereas each step from the fifth on accounts for more
than 10% of the price gap. These results suggest that the shape of the book is
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Cao, Hansch, and Wang
TABLE II
Summary Statistics of the Shape of the Limit-Order Book
Length (%)
Height (%)
Height (Cents)
Steps
Buy
Sell
Buy
Sell
Buy
Sell
1
2
3
4
5
6
7
8
9
10
11.97
13.23
12.06
11.04
10.59
9.91
9.55
9.06
8.80
3.80
11.94
12.67
11.56
10.77
10.49
10.16
9.87
9.58
9.52
3.43
5.07
8.55
9.25
9.84
10.24
10.63
10.95
11.28
11.71
12.48
5.23
8.97
9.59
10.12
10.45
10.62
10.71
10.88
11.38
12.06
1.41
2.47
2.85
3.18
3.45
3.66
3.66
3.76
3.92
4.06
1.41
2.39
2.85
3.33
3.69
4.05
4.33
4.44
4.65
4.88
Note. Reported above are, respectively, the cross-sectional averages of relative step length and height of the order
book from steps 1 to 10. Relative step length is measured as the number of shares on a step as a fraction of the total
number of shares in the first ten steps. Relative step height is measured as the price difference between a step and its
previous step, divided by the price gap between step 10 and mid inside price (MID). The cross-sectional average of the
absolute step height in cents is also reported. For the first step, the price of its previous step is set to be MID.
dense from the beginning to step 5. A denser section of the book represents higher
liquidity in that section as more shares are offered with less price gaps. Figure 1
demonstrates the shape of the average book in the authors’ sample.
To combine the price aspect and the quantity aspect of the book, the
authors use a weighted price defined as
n2
WPn1n2 d d
s s
a jn1 (Qj Pj QjPj )
n2
d
s
a jn (Qj Qj )
,
n1 n2.
(1)
1
When n1 n2 1, WPn1n2 is WP1, the weighted average mid-quote:
WP1 QdiP1d Qs1P1s
Qd1 Qs1
.
(2)
A measure similar to WP1 is the simple average of the best bid and ask,
i.e., the mid-quote MID:
MID P1d P1s
.
2
(3)
The value of WP1 will change if the height or length of the first step of the
book changes, whereas WPn1n2 changes if any of the steps between n1 and n2
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Open Limit-Order Book
150
Ask
100
Ask depth at the first step
Price (%)
50
Inside spread
0
0
50
20
40
60
100
120
Bid depth at the first step
Bid
100
150
80
Depth (%)
FIGURE 1
The shape of the average limit-order book for the sample stocks. This figure shows the shape of the
average limit-order book based on relative step length and height (in %) for the 100 most actively
traded stocks on the Australian Stock Exchange. The sample period spans from March 1 to March
31, 2000. Relative step length (in %) is measured as the number of shares on a step as a fraction of
the total number of shares in the first ten steps. Relative step height (in %) is measured as the price
difference between a step and its previous step divided by the price gap between step 10 and mid
inside price (MID). For the first step, the price of its previous step is set to be MID.
experience a change in either height, length, or a combination of both. The
authors compute WP1 and MID by using information that has traditionally
been available to traders, namely the best bid and offer prices with their associated depths. WP n1n2 is an average price between any two steps on the book,
weighted by the number of shares at each step. It summarizes all information
contained in the order book from step n1 to n2.3
An Error Correction Model and the Information
Share of the Order Book
To examine the marginal contribution of the book beyond the first step toward
price discovery, the authors employ the methods developed by Hasbrouck
Although WPn1n2 is designed to summarize the book information, it is not perfect: Two books with different
combinations of prices and depths may have the same value of WPn1n2 .
3
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Cao, Hansch, and Wang
(1995) to assess the information content of different price series. Specifically,
the authors consider three prices, MID, P, and WP2–10, that are derived from the
same limit-order book.4 The last transaction price, P, is included to further
alienate the information share of the book from what has traditionally been
available to investors. The authors examine whether the order book provides any
additional information after controlling for MID and the last transaction price P.
The methodology used to estimate the information share of different price
series is well established. For details, the reader is referred to Hasbrouck
(1995), DeJong (2002), and Huang (2002).
Let Xt be a vector of the three related pries, MID, P, and WP2–10. Although
each individual series is nonstationary, they are cointegrated and share a common stochastic trend because they are all prices of the same underlying security.
As a result, the difference between any two prices is stationary.5 The multivariate
price process can be written in an error correction form as
k1
¢Xt azt1 a i ¢Xti et
(4)
i1
where zt1 bXt1 are the error correction terms and k is the order of the original value at risk (VAR) of Xt. The authors do not include deterministic terms
for clarity of exposition. The Granger representation theorem by Engle and
Granger (1987) proved that cointegrated variables can be represented as a vector moving average through the use of the Wold decomposition theorem:
i0
ji1
¢Xt °(1)et (1 L) a a a ° j bLiet
(5)
where °(1) (In g i1 ° i ) . The sums of all the moving average coefficients
are in the matrix (1). Hasbrouck (1995) defined the measure of information
share that can be attributed to price series j as
Sj 4
° 2j © jj
°©°
(6)
MID is widely used as a measure of the true value of a stock. As a robustness check, the MID was replaced
with WP1 and it was found that the results were qualitatively similar. To save space, these results are omitted
but are available from the authors.
5
The authors tested and found that the individual series were nonstationary and cointegrated using augmented Dickey Fuller tests and Johansen’s (1988) procedure.
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Open Limit-Order Book
27
where j is the jth element of and is any row in (1). jj is the jth diagonal element of and is the variance–covariance matrix of the innovations t.
This information share is uniquely defined if the price series do not exhibit
contemporaneous correlation, i.e., if is a diagonal matrix. In the presence
of contemporaneous correlation, Hasbrouck (1995) proposed a Cholesky
decomposition procedure for , similar to the prediction error variance decomposition in VARs:
g FF
(7)
where F is a uniquely defined triangular matrix that orthogonalizes the price
innovations to
et Fht
(8)
where ht has zero mean and identity variance–covariance matrix. The information share of a price j thus computed depends on the ordering of the list of the
prices. It is bounded between a minimum and a maximum value, conditional
on whether j is listed as the last or first variable in Xt. The use of high-frequency
intraday data in the estimation can reduce the gap between the minimum and
maximum information share. Following Hasbrouck (2003), the authors sample
their order-book data at second-by-second intervals in this section, and compute the average of the minimum and maximum information share. The procedure of using the average of the minimum and maximum information share as
a proxy for the information share is widely adopted in the literature (see Booth,
Lin, Martikainen, & Tse, 2002).
Results
For each of the 100 stocks, the authors estimate the error correction model and
obtain the maximum and minimum of the Hasbrouck information share. Table III
reports the cross-sectional distributions of these estimates. Panel A reports
results based on the three price series MID, WP2–10, and P. It shows that the
information share of MID is the largest—the cross-sectional average is 54.50%,
whereas the average information shares of WP2–10 and P are 22.47 and 23.15%,
respectively. Although the top of the book as represented by MID contributes
the most to price discovery, the additional information share of WP2–10 beyond
MID and P is considerable. Judged by the reported standard deviations, the
authors note that the estimates of information shares are statistically significant.
WP2–10 aggregates nine price steps of the book and the follow-up question
is whether these nine steps contribute evenly, or if there is a specific section of
the book that is more informative than the others. To answer this question, the
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Journal of Futures Markets
Max.
Ave.
Min.
Max.
P
DOI: 10.1002/fut
Min.
53.40
11.14
53.95
Max.
MID
55.60
10.19
56.02
Ave.
54.96
54.50
Min.
22.33
7.02
22.33
Max.
P
23.97
8.16
23.62
Ave.
22.98
23.15
Ave.
49.19
12.36
50.53
51.27
11.35
51.68
51.11
50.23
20.55
6.62
20.69
22.21
7.68
22.43
21.56
21.38
9.76
4.84
9.24
Min.
21.62
10.50
18.72
Min.
12.29
6.48
10.95
Max.
WP2–4
23.31
11.03
20.63
Max.
WP2–10
10.10
11.03
Ave.
19.68
22.47
Ave.
16.36
8.7
14.69
Min.
18.83
10.47
16.40
Max.
WP5–10
15.55
17.60
Ave.
where X (MID, P, WP2–10) in Panel A and X (MID, P, WP 2–4, WP 5–10) in Panel B. k is the number of lags determined by AIC information criterion. MID is the bid–ask mid-price,
WP n1n2 is the volume-weighted average price from steps n1 to n2 of the limit-order book, and P is the last transaction price. The maximum (minimum) contribution of a price to the variance of the common factor’s innovation is when it is the first (last) variable in the Cholesky factorization. The reported numbers are in percentages. AIC, Akaike Information Criterion.
i1
¢Xt azt1 a i ¢Xti et
k1
Note. For each of the 100 sample stocks, the Hasbrouck (1995) information shares are estimated. Reported above are the cross-sectional average, standard deviation, and median
of the information-share estimates for two sets of price series. The estimated error correction model is
Mean
SD
Median
Panel B: Estimates of information share (in %) using MID, P, WP2–4, and WP5–10
Mean
SD
Median
Panel A: Estimates of information share (in %) using MID, P, and WP2–10
Min.
MID
TABLE III
Estimates of the Hasbrouck (1995) Information Shares
28
Cao, Hansch, and Wang
Open Limit-Order Book
authors partition WP2–10 into WP2–4 and WP5–10, and re-examine the error correction model using a vector of four variables X (MID, WP2–4, WP5–10, P).
Panel B of Table III reports that the results for P change little—its information
share is 21.38%. The information share of MID is still the largest (50.23%),
whereas the information share of WP2–4 and WP5–10 are 11.03 and 17.60%,
respectively.
The larger information share of the later section of the book (e.g., WP5–10)
reaffirms the importance of evaluating the orders along the limit-order book.
Order activities at or near the top of the book could be unrelated to new information. Hasbrouck and Saar (2002) documented the presence of orders used
to fish for hidden orders or to spoof the traders on the other side of the market.
A seller can submit a sell order priced just above the best bid price fishing for
trading against any hidden buy orders at the better price level. Other times, a
seller may submit a large buy order that betters the current best buy price hoping to entice other buyers to match or even outbid so as to sell to them.
Whether somebody on the buy side falls into the trap or not, the “faked” buy
order will be cancelled by the seller within a second or two. This spoofing strategy was a heavily debated practice on the Eurex system in 2004, as a flipper
profited handsomely from posting flipping bids and offers on the Bobl and
Schatz interest rate futures contracts (Financial Times, 2004/4/19). Hence the
top of the book may be very active but polluted by these “fishing” and/or spoofing actions. The later section of the order book may contain orders with more
“stable” and less “noisy” information.
As a robustness check, the authors re-estimate the Hasbrouck information
share for each stock using the order-book data, sampled every five minutes. The
authors’ results indicate that the average information share of WP2–10 is
25.02%, which is close to the 22.47% reported in Panel A of Table III. As a result
of sampling at a lower frequency, the difference between the minimum and
maximum information share is slightly larger. Overall, the authors results are
consistent with Hypothesis 1 and suggest that orders behind the best bid and
ask make a modest contribution to the price discovery.
ORDER-BOOK INFORMATION AND
SHORT-TERM STOCK RETURNS
Methodology
In this section, the authors investigate whether the order-book information
(e.g., the demand and supply schedule) is associated with future short-term
returns. In the literature, there is ample evidence of short-term predictability in
stock returns. It is conceivable that some information contained in the order
book (e.g., the imbalance between demand and supply schedules) may be useful
Journal of Futures Markets
DOI: 10.1002/fut
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30
Cao, Hansch, and Wang
in forecasting short-term returns. For dealer markets, the theoretical model
of Cao, Evans, and Lyons (2006) showed that a dealer’s superior knowledge of
market demand and supply conditions helps them forecast price changes.
However, in their study, the information on order flows is private, whereas the
order book under the authors’ investigation is public. The question the authors
ask is whether the public information on the book is associated with short-term
future returns.
The authors first examine the relation between five-minute returns and
lagged order-book statistics that are constructed from the demand and supply
schedules. Snapshots of the order book at five-minute intervals are taken to
strike a balance between the desire to have a large number of observations and
the need to allow the share price to experience a meaningful change between
any two subsequent observations. The authors experiment with one-second,
one-minute, five-minute, and ten-minute samples and find that the five-minute
sample strikes the best balance. As short-term returns are serially correlated,
the authors pre-whiten returns to focus on the innovation in returns. The
return innovation is used as the dependent variable in the regression analysis
because the innovation captures the unpredictable component of the return.
Specifically, the authors obtain innovation in return by using an AR(5) model
for each sample firm6:
5
rt a0 a airti e*t
(9)
i1
where rt is the five-minute mid-price (MID) return at t and e*t the return innovation. The independent variables include the inside spread (Spread), the trade
imbalance (Timb), and the imbalance in the length (quantity) and height
(price) of the order book. Timb is measured as the imbalance between the
executed buy and sell volumes in a five-minute period. Buy volume and sell volume are classified when marketable buy orders and sell orders consume limit
orders sitting on the other side of the book. In a sense, Timb aggregates the net
transaction volume every five minutes. The authors include Spread and Timb to
control for effects of the top of the book that investors usually have access to.
For each step j, let QRj and HRj denote the imbalance in the length and height:
QRj 6
Qjs Qjd
Qjs Qjd
,
j 1, p , 10
(10)
On the basis of the Akaike Information Criterion, the authors find that an AR model with five lags is sufficient for the sample firms.
Journal of Futures Markets
DOI: 10.1002/fut
Open Limit-Order Book
HRj s
d
) (Pjd Pj1
)
(Pjs Pj1
s
d
(Pjs Pj1
) (Pjd Pj1
)
,
j 2, p , 10.
31
(11)
Intuitively, QR (and HR) can be interpreted as the step-wise scaled imbalance in quantity (and price) between the demand and supply schedules.
The authors’ first set of regressions contains ten regressions; each includes
the book information up to step n where n 1, 2, . . . , 10:
n
n
e*t a0 d0Timbt1 b0Spreadt1 g1QR1,t1 a bjHRj,t1 a gjQRj,t1 ht. (12)
j2
j2
The list of the independent variables starts with Timbt1 and Spreadt1.
The authors add QR1 when n 1, and QRn and HRn for n 2, 3, . . . , 10. The
regression on a stock-by-stock basis is run and results are reported based on
the cross-sectional averages. As the objective is to investigate whether the
book beyond the first step helps to predict future returns, the fact that
whether the average Adjusted R2 increases as more steps of the book are
included in the regression is examined. The Adjusted R2 is reported because its
change summarizes the role that any additional book information may have in
explaining the dependent variable, while controlling for the number of independent variables.
The authors briefly discuss the anticipated relation between stock returns
and book imbalance. Intuitively, return is predicted to be negatively related to
QRj,t1 as the excess supply drives the share price down when more shares are
submitted to the supply side. Furthermore, return is expected to increase with
HRj,t1 because smaller price increments on the demand side suggest more
interest in purchasing, rather than selling shares. Several studies on order
placement strategies document a relation between the status of the order book
and future order submissions (see Biais, Hillion, & Spatt, 1995; Cao, Hansch, &
Wang, 2008; Foucault, 1999; Griffiths, Smith, Turnbull, & White, 2000;
Hollifield, Miller, & Sandas, 2004; Parlour, 1998; Ranaldo, 2004). These studies find that a large depth at the buy (sell) side of the book encourages more
market buy (sell) orders. These market orders consume limit orders on the
other side of the order book and drive the price higher (lower). It is the link
between the book and order placement strategies that connects future price
movement and current book status.7
Another way to capture the imbalance in book length and height is to
consider the demand and supply side of the book separately. The authors use
7
The snapshot of the limit-order book represents the static view of the book. It is an aggregation of the order
flows within a certain time-frame. The higher the frequency at which the snapshots are taken, the closer they
represent the dynamic order flows.
Journal of Futures Markets
DOI: 10.1002/fut
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Cao, Hansch, and Wang
the height and length of steps on the demand and supply sides (e.g.,
Qdj , Qsj, §dj ,§js) as independent variables and run a second set of regressions for
n 1,2, . . . ,10:
n
d
e*t a0 d0 Timbt1 b0 Spreadt1 a gd,j Qj,t1
j1
n
n
n
j1
j2
j2
s
a gs,j Qj,t1
a bd,j §dj,t1 a bs,j §sj,t1 ht.
(13)
In addition to the imbalance in book length and height, the authors use
price impact measures as independent variables. Price impact is measured ex
ante as a cost of trading for a hypothetical trade size of q shares. Given the fact
that the average trade size varies across firms, the authors choose q as multiples
of the firm-specific average trade size Q (e.g., q 1.0Q, 1.5Q, . . . ,5.0Q). Let
LD(q) be the price impact measure on the demand side, which is defined as the
discount per share that a market-seller gets below the midpoint of the best bid
and ask:
m11
LD(q) 0.5(P1d P1s ) d d
d
d
a j1 Pj Qj Pm1Qm1
m11
and
q
d
ld
a Qi Qm1 q
(14)
i1
1
1
where the step m1 is determined according to g i1
Qdi q g i1
Qdi and
Qld
m1 is the number of shares on step m1 to fulfill the order of q shares after the
first m1 1 steps are filled. Similarly, the price impact on the supply side LS(q)
is the premium per share a market-buyer needs to pay above the midpoint of
the best bid and ask:
m 1
m
m21
LS(q) s s
s
s
a j1 Pj Qj Pm2Qm2
q
0.5(P1d P1s )
m21
and
s
s
a Qi Qm2 q.
(15)
i1
2
2
Qis q g i1
Qis and m2 is
The step m2 is determined according to g i1
not necessarily equal to m1. Intuitively, LS(q) and LD(q) are inverse measures
of liquidity. The authors compute the scaled imbalance in price impact, LR(q),
as the following:
m 1
LR(q) LS(q) LD(q)
, q g*(Q2) and
LS(q) LD(q)
m
g 2, 3, p , 10
(16)
where the hypothetical trade size q takes value of q 1.0Q,1.5Q, . . . ,5.0Q.
Journal of Futures Markets
DOI: 10.1002/fut
Open Limit-Order Book
33
The third set of regressions relies on the scaled price impact measure
LR(q), and the fourth set of regressions uses the separated price impact on the
demand and supply side as independent variables (g 2, 3, . . . , 10):
g
e*t a0 d0Timbt1 b0Spreadt1 a bjLR( jQ2) t1 ht
(17)
j2
g
g
j2
j2
e*t a0 d0Timbt1 b0Spreadt1 a bd,j LD( jQ2) t1 a bs,j LS( jQ2) t1 ht.
(18)
As smaller price impact implies better liquidity, the authors predict that
the return at t is positively related to LR(q)t1 (or LS(q)t1) and negatively related
to LD(q)t1. In other words, when there is more liquidity on the demand side,
more limit buy orders are placed at crowded buy steps, which attracts more
market buy orders, and these market orders drive up the price.
Although the authors’ empirical design intends to uncover the dynamics
between the return and lagged book information in general, it is of potential
importance to examine the association between return and the book when
there is a large asymmetry between the supply and demand. If the book is
severely imbalanced, it may reveal the excess demand or supply that allows
traders to better infer future movements of the price. To investigate this question, each firm’s observations by the imbalance in price impact LR(q) is sorted
with q 2.5Q8 and the top and bottom 5% observations from each firm is used
to re-estimate the above four sets of regressions.
Empirical Results
Table IV presents the results of the first set of regressions specified in Equation
(12). The dependent variable is the return innovation from an AR(5) model, and
independent variables include trade imbalance, inside spread, and the scaled
imbalance in quantity and price. For each firm the regression is estimated ten
times; each regression includes the book information up to step n (n 1, 2, . . . ,
10). Two samples are considered: (1) the full sample and (2) a restricted sample
with the top and bottom 5% observations sorted by LR(2.5Q).
First the cross-sectional average of Adjusted R2 is examined for the full sample. With the trade imbalance and spread as the independent variables, the average Adjusted R2 is merely 0.59%. After adding QR1 as an independent variable,
the average Adjusted R2 increases to 5.05%. When the lagged book imbalances
8
The authors experimented with other choices of q and found that their conclusion is quantitatively similar.
Journal of Futures Markets
DOI: 10.1002/fut
34
Cao, Hansch, and Wang
TABLE IV
Regression Analysis of Returns and Scaled Order Imbalances
Full Sample
Steps
Timb and
Spread
1
2
3
4
5
6
7
8
9
10
Adjusted R2
% of Significant
Coefficients With
Anticipated Signs
Restricted Sample
% of Firms
That
Pass F-Test
Adjusted
R2
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
0.59
–
100
2.37
–
100
5.05
6.55
6.76
6.83
6.91
7.00
7.03
7.08
7.16
7.22
100
72
51
39
31
27
24
21
19
18
100
82
27
16
11
15
6
11
14
9
17.40
19.87
20.87
21.08
21.55
21.79
22.17
22.76
23.13
24.15
97
47
31
23
19
15
14
13
11
11
97
37
16
5
7
5
9
12
5
17
Note. For each of the 100 sample stocks, the following regression model is estimated ten times by using the lagged order-book
information up to step n (n 1, 2, . . . ,10):
n
n
e*t a0 d0Timbt1 b0Spreadt1 g1QR1,t1 a bjHRj,t1 a gjQRj,t1 ht
j2
j2
where e* is the innovation in returns estimated by using an AR(5) model, Timb is the trade imbalance, Spread is the inside spread, QRj
is the scaled imbalance in quantity at step j, and HRj is the scaled imbalance in price at step j. Each regression model is estimated for
the full sample and a restricted sample. The restricted sample is based on the top and bottom 5% of imbalanced price impact measured at 2.5* Q, where Q is the stock-specific average trade size. Reported above are the cross-sectional averages of the Adjusted R2
(in %), the percentage of coefficient estimates with anticipated signs, and the percentage of regressions (among 100) that pass the
F-test at 5% significance level. For a given step n, the null hypothesis of the F-test is that coefficients of HRn and QRn are jointly zero.
from steps 2 to 10 are included, the average Adjusted R2 goes up to 7.22%,
whereas the greatest increase occurs at step 2.
When using the top and bottom 5% observations according to LR(2.5Q), a
stronger result is found. For example, the cross-sectional average of Adjusted R2
increases from 2.37 to 17.40% for n 1, and then to 24.15% for n 10.
Unlike the full sample result, where the majority of the improvement occurs at
steps 1 and 2, the authors find a continued improvement in fitting result along
the book for the restricted sample. In comparison with the full sample result,
the explanatory power is higher for the restricted sample. In summary, the
order-book information is useful in explaining short-term future returns. This
result is particularly true when the order book shows a large imbalance.
The results reported in Table IV rely on 20 regressions for each of the 100
sample firms. Owing to space limitation, the regression coefficients and their
T-statistics are not reported. Instead, the results are summarized by presenting
the percentage of significant coefficients at the 5% significance level with the
Journal of Futures Markets
DOI: 10.1002/fut
Open Limit-Order Book
expected signs. The authors find that the range of anticipated signs of estimated
coefficients spans from 100% (if the book information in step 1 is used) to 72%
(if the book information from steps 1 and 2 is used). According to the signs of
estimated coefficients, future returns tend to be lower if more shares are submitted to the supply side. On the other hand, if buy orders are submitted at
smaller price increments than sell orders, the demand for the stock increases
and future returns tend to be higher. This latter finding is unique, and it
highlights the importance of the price dimension of the supply and demand
schedule. Without viewing the book information behind the best bid and
ask, investors may forever miss the value buried in the price dimension of the
order book.
Although the percentage of significant coefficients with the anticipated
signs drops as more variables along the book are included in the regression,
the authors find that the near orders tend to conform to the anticipation. The
faraway orders have the opposite effect but the majority of their coefficients
are insignificant. The accumulation of buy (sell) limit orders near the top of the
book attracts buy (sell) market orders as traders become aggressive, to get
their orders executed first. As a result, price is driven up (down). Therefore,
the order book, especially the section of the book that is near the top, helps
investors to predict future short-term returns. This effect persists after controlling for the autocorrelations in returns and other commonly observed variables such as inside spread and trade imbalance from past transactions.
Chordia et al. (2002) documented a positive association between aggregate
order imbalance and market return, and Chordia and Subrahmanyam (2004)
showed the same cross-sectional results in stocks. Boehmer and Wu (2006)
found that institutional investors’ trade imbalance (buy–sell) positively affects
future price movements, whereas the opposite impact holds for individual
investors’ trade imbalance. These trade imbalance effects are controlled for
and the authors’ investigation is extended beyond the top of the book and it is
found that imbalance in the existing limit orders along the book also affects
future price positively.
To test for the joint significance of the coefficients added in each step, an
F-test is conducted using 5% significance level. For a given step n, the null
hypothesis of the F-test is that coefficients of HRn and QRn are jointly zero.
Table IV reports the percentages of the 100 firms that pass the F-test in each
step. For the full sample, 82% of the sample firms pass the F-test when the
book information from step 2 is included in the model. This result suggests that
the null hypothesis that coefficients of HR2 and QR2 are jointly zero for
82 firms (among 100) should be rejected. When the book information from
step 3 is added, the null hypothesis that coefficients of HR3 and QR3 are jointly
zero for 27% of the sample firms is rejected. The drop in the F-test passing rate
Journal of Futures Markets
DOI: 10.1002/fut
35
36
Cao, Hansch, and Wang
from step 1 to 10 is consistent with the drop in the percentage of the significant coefficients and is also consistent with the gradual but small increase in
the Adjusted R2. Beyond step 4, the percentage of firms that pass the F-test
is below 20%, indicating that coefficients associated with HRn and QRn
(n 5, 6, . . . ,10) are generally insignificant.
Table V presents estimation results of the second set of regressions (the
model is provided in Equation (13)). When using the height and length of steps
on the demand and supply sides as independent variables, the null hypothesis
of the authors’ F-test is that all coefficients added in step n are jointly zero. The
authors find that the results reported in Table V are consistent with those in
Table IV. Specifically, the average Adjusted R2 for the full sample increases from
0.59 to 6.31% (when n 10). The change in the average Adjusted R2 is from
2.37 to 28.02% (when n 10) for the restricted sample. Turning to the percentage of coefficient estimates with anticipated signs, the authors find that
TABLE V
Regression Analysis of Returns and Order-Book Step Length (and Height)
Full Sample
Steps
Timb and
Spread
1
2
3
4
5
6
7
8
9
10
Restricted Sample
Adjusted
R2
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
Adjusted
R2
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
0.59
–
100
2.37
–
100
2.94
4.52
4.88
5.09
5.24
5.38
5.57
5.74
5.96
6.31
93
59
41
31
25
22
20
18
17
16
96
76
25
17
17
18
21
19
25
28
12.85
18.11
19.79
21.31
22.92
23.58
24.75
25.48
26.65
28.02
93
59
41
31
25
22
20
18
17
16
88
51
17
18
10
10
12
13
12
18
Note. For each of the 100 sample stocks, the following regression model is estimated ten times by using the order-book information
up to step n (n 1, 2, . . . ,10):
n
n
n
n
e*t a0 d0Timbt1 b0Spreadt1 a gd,jQdj,t1 a gs, jQsj,t1 a bd, j §dj,t1 a bs, j §sj,t1 ht
j1
j1
j2
j2
where e* is the innovation in returns estimated by using an AR(5) model, Timb is the trade imbalance, Spread is the inside spread,
Qdj (Qsj ) is the length of step j on the demand (supply) side, and §dj (§sj ) is the height of step j on the demand (supply) side of the order
book. Each regression model is estimated for the full sample and a restricted sample. The restricted sample is based on the top and
bottom 5% of imbalanced price impact measured at 2.5* Q , where Q is the stock-specific average trade size. Reported above are the
cross-sectional averages of the Adjusted R2 (in %), the percentage of coefficient estimates with anticipated signs, and the percentage
of regressions (among 100) that pass the F-test at 5% significance level. For a given step n, the null hypothesis of the F-test is that
all coefficients added in step n are jointly zero.
Journal of Futures Markets
DOI: 10.1002/fut
Open Limit-Order Book
37
the results reported in Table V are comparable to those in Table IV. The percentages of firms that pass the F-test are larger than those in Table IV for both
the full and restricted samples. Taking the restricted sample as an example,
when the book information from step 4 is added, the authors reject the null
hypothesis that all coefficients added in step 4 are jointly zero for 18% of the
sample firms, whereas the same test in Table IV has only a 5% passing rate.
The results of the third set of regressions are provided in Table VI.
These regressions intend to uncover the relation between returns at t and price
impact (liquidity) measures along the book at t 1. For a given trade size
q g*Q2, the null hypothesis of the F-test is that bg is zero. For the full sample, the authors show that the average Adjusted R2 is 0.59% with trade imbalance and spread as the only two independent variables. It increases to 4.75% at
q Q and then to 6.56% at q 5Q when the scaled price impact measures
are used as additional explanatory variables. Using the restricted sample, the
authors find that the average Adjusted R2 increases from 2.37 to 20.40%.
The majority of the coefficient estimates have the anticipated signs. This result
TABLE VI
Regression Analysis of Returns and Scaled Imbalance in Price Impact
Full Sample
q
Timb and
Spread
1.0Q
1.5Q
2.0Q
2.5Q
3.0Q
3.5Q
4.0Q
4.5Q
5.0Q
Adjusted
R2
Restricted Sample
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
Adjusted
R2
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
0.59
–
100
2.37
–
100
4.75
5.42
5.88
6.20
6.46
6.63
6.78
6.90
6.98
100
38
28
16
13
12
10
9
7
100
71
64
44
40
34
27
23
13
17.48
18.73
19.74
19.82
19.95
20.18
20.16
20.44
20.40
98
13
9
5
5
5
4
4
4
98
24
18
9
8
7
5
7
3
Note. For each of the 100 sample stocks, the following regression model is estimated nine times by using the lagged price impact
measures:
g
e*t a0 d0Timbt1 b0Spreadt1 a bjLR(g*Q2) t1 ht
j2
where e* is the innovation in returns estimated by using an AR(5) model, Timb is the trade imbalance, Spread is the inside spread, and
LR(g*Q2) is the scaled imbalance in price impact for a hypothetical trade size q g*Q2 and g 2, 3, . . . ,10. Each regression
model is estimated for the full sample and a restricted sample. The restricted sample is based on the top and bottom 5% of imbalanced
price impact measured at 2.5* Q , where Q is the stock-specific average trade size. Reported above are the cross-sectional averages
of the Adjusted R2 (in %), the percentage of coefficient estimates with anticipated signs, and the percentage of regressions (among
100) that pass the F-test at 5% significance level. For a given trade size q g*Q2 , the null hypothesis of the F-test is that bg is zero.
Journal of Futures Markets
DOI: 10.1002/fut
38
Cao, Hansch, and Wang
TABLE VII
Regression Analysis of Returns and Price Impact Measures
Full Sample
q
Timb and
Spread
1.0Q
1.5Q
2.0Q
2.5Q
3.0Q
3.5Q
4.0Q
4.5Q
5.0Q
Restricted Sample
Adjusted
R2
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
Adjusted
R2
% of Significant
Coefficients With
Anticipated Signs
% of Firms
That Pass
F-Test
0.59
–
100
2.37
–
100
5.05
6.01
6.55
6.88
7.21
7.48
7.68
7.90
8.02
96
29
21
14
12
11
10
9
9
99
72
61
37
38
36
21
28
18
17.44
19.80
21.64
22.59
23.12
23.64
24.37
24.73
25.38
96
29
21
14
12
11
10
9
9
93
31
29
21
13
8
17
10
15
Note. For each of the 100 sample stocks, the following regression model is estimated nine times by using the lagged price impact
measures:
g
g
e*t a0 d 0Timbt1 b0Spreadt1 a bd, jLD(g*Q2) t1 a bs,jLS(g*Q2) t1 ht
j2
j2
where e* is the innovation in returns estimated by using an AR(5) model, Timb is the trade imbalance, Spread is the inside spread,
and LD(g*Q2) and LS(g*Q2) are price impact measures on the demand and supply side for a hypothetical trade size q g*Q2
and g 2,3, . . . ,10. The regression model is estimated for the full sample and a restricted sample. The restricted sample is based
on the top and bottom 5% imbalanced price impact measured at 2.5* Q , where Q is the stock-specific average trade size. Reported
above are the cross-sectional averages of the Adjusted R2 (in %), the percentage of coefficient estimates with anticipated signs,
and the percentage of regressions (among 100) that pass the F-test at 5% significance level. For a given trade size q g*Q2 , the
null hypothesis of the F-test is that bd,g and bs,g are jointly zero.
suggests that stock return increases when the demand side is more liquid than
the supply side. The better liquidity on the demand side is the result of demand
outweighing supply. Finally, the percentages of firms that pass the F-test are
larger than 25% for the full sample for all trade sizes (with two exceptions).
Taking the trade size q 2Q as an example, the authors reject the null hypothesis that b2 is zero for 64% of sample firms. Therefore, the coefficient of b2 is
significant for majority of the sample firms.
The authors present the results of the fourth set of regressions in Table VII.
In this table, measures of the demand- and supply-side price impact enter the
regression model as separate variables. These results are slightly stronger than
those reported in Table VI and reinforce the authors’ earlier findings. Overall,
the regression results indicate that returns are significantly related to the
lagged order-book information after controlling for autocorrelations in return,
the inside spread, and the trade imbalance. Consistent with Hypothesis 2, the
book information, especially the book information derived from steps 2 to 4, is
useful and does provide additional explanatory power. Though not as strong as
Journal of Futures Markets
DOI: 10.1002/fut
Open Limit-Order Book
the results reported in Table III, the fact that the information-share analysis
relates to the process of price discover, which may take longer than five minutes, is understood, whereas the price prediction is for the next five-minute
interval.
CONCLUSION
In spite of the success of limit-order books in financial markets in the United
States and around the world, empirical research on the information content of
the order book is sparse and only emerging. The academic literature has customarily used the quoted mid-price as a proxy for the true asset value when
considering dealer markets, or when order-book information is not available.
The value of the information content beyond the first price step of the book is
largely unexplored.
This article examines the value of the order book from two perspectives:
(1) In comparison with the best bid and ask prices and their depths, the
authors ask whether investors can make better estimations about the true value
of the underlying stock by using book information beyond the first step, and
(2) they ask whether future short-term returns are associated with current
demand and supply schedules.
Our empirical evidence indicates that the order book beyond the first step
is moderately informative about the true value of the asset. According to the
authors’ estimates of the Hasbrouck (1995) information share for the 100 sample stocks, it is found that the contribution of the order book beyond the best
bid and offer is significant and is approximately 22%. In addition, the authors
find that the lagged book information behind the best bid and ask is significantly related to future returns. This is particularly true for a restricted sample
with an extremely imbalanced order book.
The authors’ results have important implications given the substantial
changes that financial markets have experienced in their regulatory framework
and competitive landscape in the recent past. The reduction in the minimum
price variations from eighths to sixteenths and subsequently to decimals leads
to a reduction in the quoted depth as a large number of orders have been shifted to hide behind the quotes. As a result, pre-trade transparency has been
demanded by investors. ECNs successfully satisfy investors’ request by disclosing the order book (to a certain degree), and so they are becoming more and
more popular in the trading landscape. Recently, in 2005, the NYSE–Archipelago
merger and the Nasdaq/INET acquisition once again pushed the two most popular ECNs on the same stage with the two biggest traditional market places.
The pre-trade transparency offered by many of these open book trading platforms will certainly be exploited by sophisticated traders. The order book’s
Journal of Futures Markets
DOI: 10.1002/fut
39
40
Cao, Hansch, and Wang
information share and its predictive power for short-term price movements can
help accelerate the overall process of price discovery and increase the overall
welfare for investors at large.
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